Many excitable tissues are able to develop action potentials in the absence of any salt of univalent cation in the external medium. Osterhout and his associates' have shown that Nitella cells, which have been rendered inexcitable by prolonged immersion in distilled water, regain their excitability when calcium salts are added to the external medium. Fatt and Katz,2 Hagiwara, Chichibu, and Naka,...

The convolution of convex harmonic univalent functions in the unit disk, unlike analytic functions, may not be or even univalent. main purpose this work is to develop previous in...

The aim of this paper is two-fold. First, to give a direct proof for the already established result of Styer which states that a univalent geometrically starlike function f is a univalent annular starlike function if f is bounded. Second, to show that the boundedness condition of f is necessary, thus disproving a conjecture of Styer.

1 Presented by We construct a function f (z), univalent and starlike in the unit disc, with some interesting geometric and analytic properties. It turns out that its convolutions f * λn with a specific class of univalent polynomials λn(z) are not subordinate to the function itself. This provides a counterexample to a result of Greiner and Ruscheweyh.

We show that the univalent local actions of the complexification of a compact connected Lie group K on a weakly pseudoconvex space where K is acting holomorphically have a universal orbit convex weakly pseudoconvex complexification. We also show that if K is a torus, then every holomorphic action of K on a weakly pseudoconvex space extends to a univalent local action of KC.

We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category $\mathbb{EFF}$. Path categories are categories of fibrant objects in the sense of Brown satisfying two additional properties and as such provide a context in which one can interpret many notions from homotopy theory and Homotopy Type Theory. Within the path category $\mathbb{EFF}$ one can i...

We show by elementary means that every Kan fibration in simplicial sets can be embedded in a univalent Kan fibration. Mathematics Subject Classification 55R15 · 55R35 · 55U10 · 18C50

Given two univalent harmonic mappings f1 and f2 on D, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for f3 = (1−s)f1+sf2 to lift to a minimal surface for s ∈ [0, 1]. We then construct such mappings from Enneper’s surface to Scherk’s singularly periodic surface, Sckerk’s doubly periodic surface to the catenoid, and ...